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Exploring Stellar Systems with GRAPE: N-body Methods and Hybrid Approaches for Dense Clusters

This introduction delves into the GRAPE numerical methods for dense stellar systems, covering N-body simulations, Fokker-Planck integration, and Monte-Carlo techniques. Learn about the evolution of GRAPE machines, their applications in various scientific fields, and constructing GRAPE clusters. Discover the Korean GRAPE Consortium's involvement, proposed research topics, and future plans in the realm of galactic and stellar dynamics.

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Exploring Stellar Systems with GRAPE: N-body Methods and Hybrid Approaches for Dense Clusters

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  1. Introduction to the GRAPE

  2. Numerical Methods for Dense Stellar Systems • N-body : direct integration of the equations of motion • Fokker-Planck : direct integration of the Fokker-Planck • equation • Monte-Carlo : particle-based method which uses • Monte-Carlo to apply relaxation • in the Fokker-Planck approximation • Gas model : cluster modeled as conducting gas • Hybrid methods : gas+MC, FP+N-body

  3. The GRAPE project • GOAL : • Design and build specialized hardware for • simulation of stellar systems. • Rationale : • You can do larger simulations (better resolution) • for the same amount of money.

  4. History of the GRAPE TABLE-1 Low-Precision machines Machine Year Peak speed GRAPE-1 1989 240 Mflop/s, GRAPE-3 1991 15 Gflop/s GRAPE-5 1998/9 ~ 1Tflop/s TABLE-2 High-Precision machines Machine Year Peak speedGRAPE-2 1990 40Mflop/s HARP-1 1993 180 Mflop/s GRAPE-4 1995 1 Tflop/s GRAPE-6 2002 64 Tflop/s

  5. Sciences with the GRAPE • Solar system / Planetary formation • Star-forming region / Open clusters • Globular clusters • Galactic dynamics/ Galactic nuclei • Galaxy formation • Star formation • Clusters of Galaxies / Cosmology (CDM halo)

  6. More than just N-body • SPH • “GRAPE-SPH” - Nakasato & Nomoto ,Matthias Steinmetz & Klaus Dolag ,Volker Springe • “Tree-GRAPE-SPH” • MHD“Grape-MSPH” - Dolag et al. (1991, 2002) • SPH simulations of magnetic fiels in galaxy clusters. • K. Dolag. (A&A 348, 351, 1999) • PM • “Grape + PM” - Andreas Huss

  7. Constructing a GRAPE Cluster • 6,900,000 Yen for each GRAPE6-BLX64 board • Each BLX64 has 4 GRAPE chips • Total 132 Gflops • 3,000,000 Won for each host PC • Two 2.0GHz dual-core Xeons, 1 GB memory • 3,800,000 Won for one server PC • Two 2.0GHz dual-core Xeons, 1 GB memory

  8. The Korean GRAPE Consortium • 이형목 교수님 : 구매 진행 중 • 2007 : 4 BLX64’s • 2008 : 4 BLX64’s or DR ? • SRC 멤버 : 3월 구매 예정 • 2007 : 4 BLX64’s • 2008 : 4 BLX64’s or DR ? • 공동연구 과제 신청? • 학진 기초과학 공동연구 : 1억/년, 최대 3년 (3월 신청) • 과학재단 특정기초 :1억/년, 최대 5년 (5월 신청)

  9. Proposed Research Topics • Galactic Dynamics • Galactic warps : triaxial live halo • Galaxy interaction and evolution • Galactic Center Hydrodynamics • 200-pc molecular ring (the Central Molecular Zone) • 5-pc molecular ring (the Circumnuclear Ring) • Stellar Dynamics • Evolution of the globular cluster mass function • The Arches cluster • Future Plans • Development of new codes (Monte Carlo simulations + GRAPE) • Planetary dynamics

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